title: Evaluation the reflection coefficient of polymeric membrane in concentration polarization conditions.
abstract: BACKGROUND
  The reflection coefficient of the membrane (sigma) is one of the basic parameters of the polymer membrane transport. Classical methods used to determine this parameter require intensive mixing of two solutions separated by a membrane to eliminate the effects of concentration polarization. In the real conditions, especially in biological systems, this requirement is challenging. Thus, concentration boundary layers, which are the essence of the phenomenon of concentration polarization, form on both sides of the membrane.
  
  
  OBJECTIVE
  The main aim of this paper is to determine whether the value of reflection coefficient in a concentration polarization conditions depend on the concentration of solutions and hydrodynamic state of concentration boundary layers.
  
  
  METHODS
  In this paper, we used the hemodialysis membrane of cellulose acetate (Nephrophan) and aqueous glucose solutions as the research materials. Formalism of nonequilibrium thermodynamics and Kedem-Katchalsky equations were our research tools.
  
  
  RESULTS
  Derived mathematical equations describe the ratio of reflection coefficients in a concentration polarization conditions (sigmaS) and in terms of homogeneity of the solutions (sigma). This ratio was calculated for the configuration in which the membrane was oriented horizontally. It was shown that each of the curves has a biffurcation point. Above this point, the value of the reflection coefficients depended on the concentration of the solution, the configuration of the membrane system and the hydrodynamic concentration boundary layers. Below this point, the system did not distinguish the gravitational directions.
  
  
  CONCLUSIONS
  on coefficient of the hemodialysis membrane in a concentration polarization condition (sigmaS) is dependent on both the solutions concentration and the hydrodynamic state of the concentration boundary layers. The value of this coefficient is the largest in the state of forced convection, lower--in natural convection state and the lowest in diffusive state. Obtained equations may be relevant to the interpretation of membrane transport processes in conditions where the assumption of homogeneity of the solution is difficult to implement
authors.affiliation: Department of Informatics for Economics, University of Economics in Katowice. kornelia.batko@ue.katowice.pl
authors.forename: Kornelia
authors.initials: K
authors.lastname: Batko
authors.forename: Izabella
authors.initials: I
authors.lastname: Slezak-Prochazka
authors.forename: Andrzej
authors.initials: A
authors.lastname: Slezak
mesh_terms: D002482:Cellulose / Q000031:analogs & derivatives* / Q000737:chemistry; D004058:Diffusion; D057446:Hydrodynamics; D008422:Materials Testing; D008567:Membranes, Artificial; D008956:Models, Chemical; D009995:Osmosis; D010539:Permeability; D011108:Polymers; D006435:Renal Dialysis / Q000295:instrumentation*; D013499:Surface Properties
chemical_list: D008567:Membranes, Artificial; D011108:Polymers; C005062:acetylcellulose; D002482:Cellulose